The Future of Theoretical Physics and Cosmology

Transcription

1 The Future of Theoretical Physics and Cosmology Celebrating Stephen Hawking's 60th Birthday Edited by G. W. GIBBONS E. P. S. SHELLARD S. J. RANKIN CAMBRIDGE UNIVERSITY PRESS

2 Contents List of contributors Preface xvii xxv 1 Gary Gibbons and Paul Shellard Popular symposium Spacetime singularities Black holes Hawking radiation Quantum gravity M theory and beyond De Sitter space Quantum cosmology Cosmology Postscript 10 Part 1 Popular symposium 15 2 Our complex cosmos and its future Martin Rees '. V The universe observed Cosmic microwave background radiation The origin of large-scale structure The fate of the universe The very early universe 30

3 vi Contents 2.7 Multiverse? The future of cosmology 36 3 Theories of everything and Hawking's wave function of the universe James Hartle Different things fall with the same acceleration in a gravitational field The fundamental laws of physics Quantum mechanics A theory of everything is not a theory of everything Reduction The main points again The problem of spacetime singularities: implications for quantum gravity? Roger Penrose Why quantum gravity? The importance of singularities Entropy Hawking radiation and information loss The measurement paradox Testing quantum gravity? 70 Useful references for further reading 73 5 Warping spacetime Kip Thome A first glimpse of the Golden Age: LISA: mapping black holes with gravitational waves The Golden Age again: colliding black holes LIGO/VIRGO/GEO: probing colliding black holes with gravitational waves Quantum behavior of human-sized objects Probing the big bang with gravitational waves Cosmic censorship: betting with Stephen Time travel 100 Useful references for further reading 103

4 Contents vii 6 Sixty years in a nutshell Stephen Hawking How it began ~ General relativity and cosmology Mach's principle and Wheeler-Feynman electrodynamics The steady state Gravity and the expanding universe Collapsing stars Hawking radiation Inflation M theory and the future Conclusion 117 Part 2 Spacetime singularities Cosmological perturbations and singularities George Ellis Part A: Cosmological perturbations Fluids and scalar fields Cosmic background radiation Issues 135 Part B: Cosmological singularities Analytic direct approach Indirect method Issues Conclusion The quantum physics of chronology protection Matt Visser ' Why is chronology protection even an issue? Paradoxes and responses Elements of chronology protection Semiclassical arguments The failure of semiclassical gravity Where we stand Energy dominance and the Hawking-Ellis vacuum

5 viii Contents conservation theorem Brandon Carter The~energy dominance condition The vacuum conservation theorem On the instability of extra space dimensions Roger Penrose The issue of functional freedom Functional freedom in higher-dimensional theories Classical instability of extra dimensions The holographic conjecture Part 3 Black holes Black hole uniqueness and the inner horizon stability problem Werner Israel The trailblazers: Moscow Cambridge Descent into the interior Internal evolution problem Spherical models The generic case Conclusions Acknowledgements Black holes in the real universe and their prospects as probes of relativistic gravity Martin Rees Stellar mass holes Supermassive holes Scenarios for black hole formation The galactic context Do the candidate holes obey the Kerr metric? Gravitational radiation as a probe 230

6 Contents ix Primordial black holes Bernard Carr Preface Historical overview PBHs as a probe of primordial inhomogeneities PBHs as a probe of cosmological phase transitions PBHs as a probe of a varying gravitational constant PBHs as a probe of gravitational collapse PBHs as a probe of high energy physics Postscript Black hole pair creation Simon Ross Constructing instantons: the C metric Calculation of the action Pair creation rate Black holes at accelerators Steve Giddings TeV-scale gravity Black holes on brane worlds Black hole decay and signatures The future of high energy physics Part 4 Hawking radiation Black holes and string theory Malcolm Perry M theory and black hole quantum mechanics Joe Polchinski A story 'Finding Stephen's mistake' The strong interaction and black holes 307

7 x Contents Playing with black strings Gary Horowitz Existence of new (vacuum) solutions Properties of the new solutions New charged black strings Open questions Conclusions Twenty years of debate with Stephen Leonard Susskind Crisis and paradigm shift Stephen's argument for coherence loss Horizon Complementarity The Holographic Principle The ultraviolet/infrared connection Counting black hole microstates De Sitter space Correlations in finite entropy systems Part 5 Quantum gravity Euclidean quantum gravity: the view from 2002 Gary Gibbons Some historical recollections The path integral The AdS/CFT correspondence The volume canonical ensemble Hyperbolic 4-manifolds Action and complexity Euclides ab omni naevo vindicatus? Zeta functions, anomalies and stable branes Ian Moss

8 Contents xi 21.2 (-functions Heat kernel coefficients Anomalies Brane worlds Outlook Some reflections on the status of conventional quantum theory when applied to quantum gravity Chris Isham The danger of a priori assumptions Alternative conceptions of spacetime Presheaves and related notions from topos theory Presheaves of propositions, and valuations in quantum theory Conclusions Quantum geometry and its ramifications Abhay Ashtekar A bird's eye view of loop quantum gravity Applications of quantum geometry Outlook Topology change in quantum gravity Fay Dowker A top down framework for topology change Morse metrics and elementary topology changes Good and bad topology change Progress on the Borde-Sorkin conjecture Looking to the future Part 6 M theory and beyond The past and future of string theory Edward Witten String theory

9 xii Contents David Gross Motivations for quantum gravity The achievements of string theory The future of string theory A brief description of string theory Michael Green Historical background String theory today Duality and M theory Future perspective The story of M Paul Townsend The supermembrane Backgrounds of reduced holonomy The sigma model limit Gauged supergravity and holographic field theory Nick Warner Gauged supergravity and a thesis project The ups and downs of maximal gauged supergravity Exploring higher dimensions Holographic field theory and AdS/CFT correspondence Bulk gravity and brane renormalization: where are the branes? Holographic renormalization group flows: an example Final comments Varieties in a NUTshell Chris Pope Four-dimensional self-dual metrics Non-compact self-dual 4-metrics Compact self-dual 4-metrics: K Special holonomy in higher dimensions Ricci-flat Kahler 6-metrics and the conifold Seven-dimensional metrics of G2 holonomy 528

10 Contents xiii 30.8 Spin(7) holonomy Conclusion Part 7 De Sitter space Adventures in de Sitter space Raphael Bousso De Sitter space Entropy and temperature of event horizons Entropy bounds from horizons Absolute entropy bounds in spacetimes with A > Quantum gravity in de Sitter space Instabilities of the Nariai solution De Sitter space in non-critical string theory Andrew Strominger with Alexander Maloney and Eva Silverstein De Sitter compactifications of super-critical string theory Metastability of the De Sitter vacuum Supergravity, M theory and cosmology Renata Kallosh Extended supergravities with ds vacua Hybrid inflation with D-branes M theory on a four-fold with G-fluxes Part 8 Quantum cosmology The state of the universe James Hartle Final theories Effective theories Directions

11 xiv Contents 35 Quantum cosmology Don Page 35.1 Motivation for a quantum state of the cosmos 35.2 The Hartle-Hawking proposal for the quantum state 35.3 Zero-loop quantum cosmology and FRW-scalar models 35.4 Real classical solutions for the FRW-scalar model 35.5 Complex classical solutions for the FRW-scalar model 35.6 FRW-scalar models with an exponential potential 35.7 Summary Quantum cosmology and eternal inflation Alexander Vilenkin Quantum cosmology The tunnelling wave function Alternative proposals for the wave function Semiclassical probabilities Comparing different wave functions Do we need quantum cosmology? Is quantum cosmology testable? Probability in the deterministic theory known as quantum mechanics Bryce DeWitt Quantum measurement Reality Signalling by permutations Equal likelihood The case of degeneracy Unequal probabilities The interpretation of quantum cosmology and the problem of time Jonathan Halliwell The classical case The decoherent histories approach to quantum theory The induced inner product The class operators Decoherence and the decoherence functional

12 Contents xv 38.7 Summary and discussion What local supersymmetry can do for quantum cosmology Peter D'Eath No-boundary state The classical Riemannian boundary-value problem Self-duality Canonical quantum theory of N=l supergravity: 'traditional variables' Canonical quantization of N=l supergravity: Ashtekar- Jacobson variables Comments Part 9 Cosmology Inflation and cosmological perturbations Alan Guth 40.1 The origin of inflationary fluctuations 40.2 The 1982 Nufneld workshop 40.3 Observational evidence for inflation 40.4 Eternal inflation 40.5 A new singularity theorem 40.6 The origin of the universe 41 The future of cosmology: observational computational prospects Paul Shellard 41.1 Empirical cosmology 41.2 The cosmic microwave sky 41.3 Cosmological perturbations and cosmic concordance? 41.4 Critical observational tests 41.5 Primordial gravitational waves 41.6 Computational prospects 41.7 Afterword and

13 xvi Contents The ekpyrotic universe and its cyclic extension Neil Turok Homage to the Ancients The ekpyrotic universe model The main problem Flatness Density perturbations Brane collisions The inter-brane potential The cyclic universe Back to the singularity Conclusions Inflationary theory versus the ekpyrotic/cyclic scenario Andrei Linde Chaotic inflation Hybrid inflation Quantum fluctuations and density perturbations From the Big Bang to eternal inflation Inflation and observations Alternatives to inflation? Ekpyrosis Cyclic universe Conclusions Brane (new) worlds Pierre Binetruy Why study brane cosmology? Life on the brane AdS/CFT correspondence Moduli fields. Moduli space approximation Cosmological constant Bulk scalars Infinite dimensions Open problems Publications of Stephen Hawking Index